Rapid prototyping is defined as computer-controlled additive fabrication, in that an object can be fabricated by the addition of material rather than conventional machining methods that rely on removal or the subtraction of material. The term “rapid” is, it will be appreciated, a relative term but one that has specific meaning within the art, in that construction of a finished three dimensional articles can take from several hours to several days, depending on the method used and the size and complexity of the model. There are many known methodologies that are employed within the general field of rapid prototyping Layered Object Manufacture (LOM) is one form of Rapid prototyping (RP) which relates to the successive layering of adhesive-coated paper, plastic, or metal laminates which are then successively glued together and cut to shape with a knife or laser cutter.
LOM, similarly to other rapid prototyping techniques, conventionally involves the use of a three dimensional (3D) computer aided design (CAD) of an object/part to be made, from which a stereolithography (STL) or other suitable format file is generated within a CAD package. The STL file is processed and in effect virtually sliced in the Z-axis at a thickness matching the thickness of the substrate material used. This creates a series of cross sections of the part and at any particular height each one has a simple two dimensional (2D) profile. A profiling, or cutting, apparatus may be used to trace the 2D profiles and thus cut the shapes onto thin sheets of raw material. In LOM, each individual thin sheet may be stacked and bonded one on top of another to produce a finished 3D object. The order of the profiling, stacking and bonding processes may be interchanged.
Colour 3D printing involves applying colour digitally to each of the layers used in the fabrication of a 3D printed article. Colour is required at the required intensity on each surface of the final 3D printed article as follows:                the front surface—the uppermost surface of the printed media        the rear surface—the underside surface of the printed media        the profiled edge—the edge of the media that has been cut according to the digital profile for that layer in the 3D article        
It is desirable that the ink is absorbed by the media layer, such as paper, through its entire thickness (referred to as strike through or print through) as each object layer requires colour throughout its volume. However, in conventional colour 3D printing, the ink tends to percolate throughout the open porosity of the media causing the image to spread beyond the initial contact area that the ink has with the media. This is particularly problematic when 3D colour printing takes place from one side of the media alone.
For example as shown in FIG. 1a, inkjet printing colour 80a onto a medium such as a powder layer 120 using a conventional 3D colour printer relies on printing from one side only. During the ink absorption process, the ink 80a spreads into the thickness of the layer 120 and continues to spread into a wider area than the original contact area, as indicated in FIG. 1b. In addition there is no physical barrier to prevent the ink to continue to spread into a previously printed layer 130 beneath the target layer 120, which may lead to an intermixing of printed layers, as illustrated in FIG. 1b. The intermixing region is designated by reference numeral 80c. Both spread of ink and layer intermixing causes a degradation in image acuity, that is, blurring of image and diffuse colours. FIG. 1c illustrates the finished object, comprising diffuse surfaces and colour mixing regions 80c. It will be appreciated such a solution, while providing colour within the 3D environment does not provide an optimal solution. In addition, referring to FIG. 1d, by printing from one side only of the media layer, it is necessary to print adjacent dots sufficiently close together so as to ensure no areas of the media layer are left unprinted particularly on the lower layer surface. By bringing ink dots together, their subsequent bleed in the X and Y in-plane will cause them to converge and produce a mixed colour typically appearing as a brown or black. To avoid colour mixing, the printing density must be reduced to avoid the intermixing of inks, and this would result in surfaces that have a lower than optimal ink drop density, as illustrated in FIG. 1e. 
In another aspect of conventional inkjet printing, the media is treated with a sizing agent or filler, to render the media physically less susceptible to the migration of ink, from the front printed side, to the rear side of the media by reducing the amount of porosity available for ink to find pathways for flow. Surface sizing agents (applied to the media surface) may be modified starches, hydro colloids such as gelatine, or alkyl ketene dimers, which are amphipathic molecules with hydrophilic ends facing the cellulose fibres, and hydrophobic tails facing out towards the ink, creating a degree of water repellency and resistance to ink flow and penetration. Typical ink used in inkjet printing uses water as the predominant solvent.
In colour 3D printing it is desirable that the ink fully saturates the media so that the paper is coloured in three dimensions. There are limitations in the types of media, such as paper, that are suitable for use in conventional LOM systems. As paper is composed of a randomly felted layer of fibre, it follows that the structure may have varying degrees of porosity. Paper is a highly porous material and contains as much as 70% air. The porosity of a sheet is an indicator of the moisture absorption capacity of the paper, or the ability of a particular sheet of paper to accept ink or water. When selecting a particular type of paper for LOM, it is therefore important to consider the porosity of the media.
Commonly, ink used in desktop inkjet printing onto paper is water based, with binders, and dyes or pigments imparting colour.
After a plurality of media object layers are formed, a profiling and layer bonding process is performed. The plurality of layers are bonded together, and then a profiling or weeding process is performed which comprises removing unwanted support material from the printed media stack to reveal the 3D printed object. Conventionally, during the weeding process, a technician performing the task has to observe a 3D model object on a computer screen as he/she removes the unwanted layers during weeding.
In colour 3D printing, there are three facets to each media layer, the horizontal front side (face up), the horizontal rear side (facing down) and the profiled (cut) vertical walls. Each surface of the finished 3D object may have varying percentages of front/back/vertical surface area exposed to light. There may be slight variations in colour intensity between the front/back surfaces when compared to the angled walls of the 3D object.
These variations may depend on the nature of the faceting of the wall (a mixture of vertical and horizontal surfaces), and may depend on two contributing factors:                1. The ink which is printed from both sides of the media layer may not penetrate to the centre of the media layer edge uniformly. This means that there will be a component of the media layer colour in the resultant visual effect, thus generally reducing colour saturation.        2. Shading due to the step caused by a media layer edge may serve to darken the printed colour. However, this is subjective and may depend on the viewing angle and the angle of the light source to the surface in question. Accordingly, it is assumed that both the light source and viewing angle are normal to the surface. In this case, shading is not a contributing factor.        
FIG. 1f illustrates a stack of printed media layers 1200 oriented with respect to a light source. The horizontal top and bottom surfaces 1200a and 1200b present themselves to the incident light with no facets and a uniform optical intensity profile. In FIG. 1g, the top surface 1200a is oriented at 30 degrees to the horizontal plane, which presents a mixture of horizontal walls 122 (predominantly) and vertical walls 124 including page edges in the step regions that reflect more light than planar, non-faceted surfaces. In FIG. 1h, the top surface 1200a is oriented at 45 degrees to the horizontal plane, which may produce a more equal mix of horizontal and vertical walls 122 and 124 and a higher frequency of steps per unit area. FIG. 1i shows steeper walls (60 degrees to the horizontal plane), which yields more vertical walls 124 than horizontal walls 122, and an increase in facets. In the last example in FIG. 1j, the surface is comprised entirely of vertical facets with the light source oriented at 90 degrees to the vertical facets. In FIG. 1j, the surface facing the incident light has a topography different to the horizontal surfaces 1200a and 1200b and is a multi-laminate structure.
A colour gamut describes the range of visual stimulus which can be represented by a device or image format, or that range which may be perceived by an input device such as a camera or indeed a human viewer. A commonly used representation is the CIE 1931 XY chromaticity diagram as shown in FIG. 1k. The axes represent the XY colour space coordinates with colour wavelengths depicted around the locus of the gamut. The larger lobe-shaped gamut represents the extents of human visual perception; also depicted is an example sRGB device gamut which is significantly smaller. The gamut for a colour printer is typically smaller again and more irregular in shape due to the use of four component inks versus the tri-stimulus sRGB space.
When attempting to print an image which is represented in a typical computer monitor output format a problem arises. A large area of the monitor gamut will not be available to the printing device so the field of gamut-mapping comes into play in transforming colours of one device gamut onto another. A naive approach would be to preserve all colours common to both gamuts and then remap all outlying colours of the input gamut to the nearest edge of the output gamut. This would preserve accuracy for some colours but for others would map all outlying values to a small set of colours along the output gamut edge. The poor visual effect which results from this means that other less colour accurate approaches are generally used.
The above description pertains to traditional 2D imagery as applied to 2D paper printers, colour monitors, etc. When considering the field of 3D-manufacturing in colour, another dimension to the above mapping arises; i.e. that of a potential colour dependency to a particular physical orientation or orientations. This may arise in Layered Object Manufacturing (LOM) based rapid-prototyping using paper, but also other 3D printing technologies. The physical orientation dependency in this case arises due to the possibility that ink may not fully penetrate the paper. This means that for a saturated colour on one or both paper surfaces there may be a component of the paper colour combining with the ink to produce an altered visual effect when viewed from the page edge.
In FIG. 1l the problem is represented for the case of a stack of bonded paper which has been duplex coloured; the inks have not fully penetrated, so the base colour of the paper is still present in the middle of the page thickness. This is not a problem in the 0° viewing angle shown as only the top-surface of the paper is visible; the effect will be the same as for a 2D print of the same colour. When viewed from the side, however, or at 90°, the paper colour component comes into play from the part of the profile where ink has not penetrated. The visual effect would be of a colour mix between the base paper colour and the printed green: something approximating a desaturated version of the original printed colour.
The effect of this de-saturation could be a visible break in colour uniformity across different angled facets of a part.
There are therefore a number of problems with colour 3D printing processes for use in LOM systems for rapid prototyping that need to be addressed.